arie bodek, univ. of rochester1 outline of a program in investigating nucleon and nuclear structure...

Arie Bodek, Univ. of Rochester 1

Outline of a Program in Investigating Nucleon and Nuclear Structure at all Q2 - Starting with P 04-001 ( PART 1 of JUPITER program)

(a) Study Nucleon Structure and Nuclear Effects(b) Provide basic measurements needed for the next generation neutrino oscillation

experiments.• Study Nuclear dependence of Rvector, F2vector and F1vector and

compare to Models (e.g. Pion excess) using P04-001data on nuclear targets.

• Update Vector Form Factors and Rvector of the large number of resonances in the Nucleon, e.g. within Rein-Seghal-Feynman Quark Oscillator model (and other resonance models) by fitting all F2 and R Electron Resonance data E94-110 (H) , E02-109 (D) (+ SLAC + photoproduction+ and other data)

* [propose to run P04-001 on nuclear targets at the same time as E02-109 (D)]

PART II- JUPITER Program: Include existing Hall B data on final states to help separate resonance and continuum on nucleon and nuclear targets (collaborate with theorists)

PART III - Collaborate with MINERvA Neutrino Experiment Improve on Inelastic Continuum modeling of Vector F2 and R (e.g. using a formalism like

Bodek/Yang) using Jlab, SLAC, H and D data, photoproduction and HERA data.Within these models, convert EM Vector Form Factor to Weak Vector Form Factors - use

the Various isospin rules I=1/2 and I=3/2 of elastic, resonance and inelastic Form Factors fits to H and D data E94-110, E02-109

Investigate if the Model predictions for Vector Scattering in neutrino reactions satisfy QCD sum rules and duality at high Q2 and Adler Vector Rum rules at ALL Q2.

Investigate if the Models predictions for Axial scattering in neutrino reactions satisfy QCD sum rules and duality at high Q2 and Adler Axial Rum rules at ALL Q2.


1. Apply nuclear corrections for DIS and resonance region to predict Neutrino and Antineutrino Vector Part on nuclei from PR 04-001 - Requires 5 days of running - Also use E99-118 and SLAC E140 and other for DIS A dependence.

2. Compare predictions to existing low statistics neutrino data and to new precise neutrino data to become available (MINERvA, and JHF- Japan) - Do the predictions from models (which satisfy all sum rules and duality) model the neutrino and antineutrino data well?

3. In parallel - Final states in nuclear targets to be investigated in a collaboration with Hall B experiments in electron experiments and in new neutrino experiments.

•Nucleon +Resonance Vector Form Factors, Vector Continuum F2 at all Q2, Rvectror =L/T in great details.

• Pion Excess and Nuclear effects on various targets in res, and quasielastic region (vector scattering) as a function of Q2

•Hadronic Final Stares in electron scattering

•Check on Current Algebra sum rules and understanding duality -

•Axial vector contribution to F2 at low Q2

•Different nuclear effects in neutrino scatt.

•Account for Raxial different from Rvector

•Hadronic final states in neutrino scattering

Things can be learned from electron scattering Things that are learned in neutrino scattering

Collaborative approach between High Energy and Nuclear Physics community

High x and low Q2 PDFs for e/neutrino, Resonance form factors, nuclear corrections1.Electron scattering exp. at JLAB P04-001 - 5 Days of DATA and -> Lots of analysis+ follow-up

with investigation of final states2.New Near Detector neutrino expts. at Fermilab-NUMI/JHF - -->Years of data e.g. MINERvA +

JHF


Radiative Corrections Checks, e.g. SLAC E140


Start with: Quasielastic: C.H. Llewellyn Smith (SLAC).Phys.Rept.3:261,1972

Vector form factors

From electron

scattering

Via CVC

Axial form factor fromNeutrino experiments

Neutrino experiments useDipole form factors with Gen=0 -Because this is what was put in the LS paper (not exactly correct)

Vector

VectorAxial

Updated recentlyBy Bodek, Budd andArrington 2003


However, quasielastic neutrino cross sections are not well measured so

Models are used to predict the cross section. Vector form factors are

Measured in electron scattering and axial form factors are exctracted from

The Q2 dependence of neutrino events (since the neutrino flux is not

Known very well in previous experiments). Note

Relastic = 4 (M2/Q2)(Ge/Gm)2


Next - Resonance Modelse.g. Current Matrix Elements from a Relativistic Quark Model

- Phys. Rev. D 3, 2706–2732(1971) R. P. Feynman, M. Kislinger, and F. Ravndal referred to as the FKR Model - A relativistic equation to represent the symmetric quark model of hadrons with harmonic interaction is used to define and calculate matrix elements of vector and axial-vector currents.

Improvements on parameters within this Resonance Model:

D. Rein and L. M. Sehgal, Annals Phys. 133, 79 (1981) ;D. Rein, Z. Phys. C. 35,

43 (1987) These are coded in MC generators - but there are also other proposed recently.

Recent models (e.g. Sato and Lee model) are more refined and includes meson cloud --> Non zero R and a better predictions for the axial couplings.


Resonance Model applied to Photo-production Electroproduction/Neutrino-production

Photoproduction: FKR: Kneis, Moorhouse, Oberlack, Phys. Rev. D9, 2680 (1974)

Electroproduction: FKR: F. Ravndal, Phys. Rev. D4, 1466 (1971)

Note, measured non L

in region comes from Pion cloud, FKR Model only Has 3 quarks L =0

for

1236 Resonance

In a simple FKR Model L =0

Harry Lee from Argonne has offered to work withUs on modeling of resonance electro-production and neutrino-production. He has done work on the Delta region: Electroproduction: Phys. Rev. C63.-55201 (2001) Neutrino productions : nucl-th/0303050 (2003)

vector

Axial

Total

Sato+Lee Neutrino Region nucl-th/0303050 More sophisticated

Electroproduction Region

Neutrinoproduction

Region


Correct for Nuclear Effects measured in e/ expt.

Comparison of Fe/D F2 dat In resonance region (JLAB) versus DIS SLAC/NMC data In TM (However, what happens at low Q2? Is it versus W or other scaling variable . What happens when R is large at low Q2 in the resonance region?

From SLAC E87, E139, E140, and Muon Scattering

(People involved in E139,E140 Bodek, Rock, Bosted are also in E03-110...

W = [Q2+B ] /[ M (1+(1+Q2/2)1/2 ) +A]

TM = [Q2 ] /[ M (1+(1+Q2/2)1/2 )]

Q2=4, Fe TargetRed=resonanceGreen = DIS

SLAC E139,E140

TMx

Fe/D

DIS

Fe/D

Res


How are PDFs Extracted from global fits to High Q2 Deep Inelastic e// Data

uV dVfrom F2

x(u u_

) x(d d)_

xF3 x(u u

_

) x(d d)_

u u_

from F2p

4

9x(u u

_

) 1

9x(d d)

_

d d_

from F2n 1

9x(u u

_

) 49x(d d)

_

nuclear effects

typically ignored

F2n 2

F2d

F2p 1

d /u from p p_

W Asymmetryd /u(x1) d /u(x2)

d /u(x1) d /u(x2)At high x, deuteron binding effects introduce an uncertainty in the d distribution extracted from F2d data (but not from the W asymmetry data). X=Q2/2M Fraction momentum of quark

MRSR2 PDFs

Note: additional information on Antiquarks from Drell-Yan and on

Gluons from p-pbar jets also used. xq is the probability that aParton q carries fractional momentum x = Q2/2M in the nucleon (x is the Bjorken Variable)

For data on nuclei, need nuclear Corrections.

Valence, Sea

Strange dist.


Duality, QCD Sum Rules, and Current Algebra Sum Rules.

Local duality and Global duality appears to work for Q2 > 1.5 GeV2 in electron scattering: This is basically a consequence of the fact that if target mass effects are included, higher twists are small and QCD sum rules are approximately true for Q2 > 1.5 GeV2 .

(e.g. momentum sum rule - quarks carry about 1/2 of the proton momentum) F2

eP, F2eN are related to PDFs

weighted by quark charges).

At high Q2, duality also seems to work for nuclear corrections.

What happens at low Q2 ?


• - = W2 (Anti-neutrino -Proton) • + = W2 (Neutrino-Proton) q0=

Adler Sum rule EXACT all the way down to Q2=0 includes W2 quasi-elastic

S. Adler, Phys. Rev. 143, 1144 (1966) Exact Sum rules from Current Algebra. Sum Rule for W2 DIS LIMIT is just Uv-Dv =1

[see Bodek and Yang hep-ex/0203009] and references therein

Vector Part of W2, 0 at Q2=0, 1 at high Q2-Inelastic

Adler is a number sum rule at high Q2

DIS LIMIT is just Uv-Dv.

=1 is

[F2()F2

()]

0

1

d[Uv()Dv()]d0

1

21

F2-= F2 (Anti-neutrino -Proton) = W2

F2+= F2 (Neutrino-Proton) = W2

we use: dq0) = d ( )d at fixed q2= Q2

Elastic Vector =1 Q2=0

Elastic Vector = 0 high Q2

Elastic gA=(-1.267)2 Q2=0

Elastic gA = 0 high Q2

Axial W2 = non zero at Q2=0

Axial W2 =1 at high Q2, Inelastic

+ Similar sum rules for W1, W3, and strangeness changing structure functions


When does duality break down Momentum Sum Rule has QCD+non- Perturbative Corrections (breaks down at Q2=0)

but ADLER sum rule is EXACT (number of Uv minus number of Dv is 1 down to Q2=0).

• In proton :• QPM Integral of F2p =• 0.17*(1/3)^2+0.34*(2/3)^2 = 0.17 (In

neutron=0.11) • Where we use the fact that • 50% carried by gluon • 34% u and 17% d quarks

Q2= 0.07 GeV2

Q2= 1 5 GeV2 Q2= 2 5 GeV2

Q2= 3 GeV2Q2= 9 GeV2

Q2= 1. 4 GeV2Q2= 0.8 5 GeV2

Q2= 0.22 GeV2Elastic peak

DIS high Q2 Integral F2p

Adler sum rule (valid to Q2=0) is the integral

Of the difference of F2/x for Antineutrinos

and Neutrinos on protons (including elastic)

Int F2P Elastic Q2 Int Inelastic

1.0000000 0 00.7775128 0.070.4340529 0.250.0996406 0.850.0376200 1.40.0055372 30.0001683 90.0000271 150.0000040 25 0.17


Tests of Local Duality at high x, high Q2 vs. Q2=0 Electron Scattering Case

• INELASTIC High Q2 x-->1.

• QCD at High Q2 Note d refers to d quark in the proton, which is the same as u in the neutron. d/u=0.2; x=1.

• F2 (e-P) = (4/9)u+(1/9)d = (4/9+1/45) u = (21/45) u

• F2(e-N) = (4/9)d+(1/9)u = (4/45+5/45) u = (9/45) u

• DIS LIMIT High Q2

• F2(e-N) /F2 (e-P) = 9/21=0.43

Different at low Q2, where Gep,Gen dominate.

• Elastic/quasielastic +resonance at high Q2 dominated by magnetic form factors which have a dipole form factor times the magnetic moment

• F2 (e-P) = A G2MP(el) +BG2

MP (res c=+1)• F2 (e-N) = AG2

MN (el) +BG2MN (res c=0)

• TAKE ELASTIC TERM ONLY• F2(e-N) /F2 (e-P) (elastic High Q2) =2N2P2 =0.47 Close if we just take the elastic/quasielastic x=1

term.

Gen/Gep (Q2=0) = 0 Since Gen=0.

Q2 = 0 ElasticLimit


On neutrons both quasielastic And resonance+DIS production possible. First resonance has different mixtures of I=3/2 And I=1/2 terms. Neutrino and electron induced production are related using Clebsch Gordon Coeff. (Rein Seghal model etc)

NEUTRINOS

On nucleons

X = 1

quasielastic

X = 1 zero1st reson

1st reson

0-

W+

P=uu duuu ( Res only state)

On protons only resonance+

DIS production possible.

NEUTRINOS

On Protons

-

N=ud dud u = (P or ) Both quasi+Res

NEUTRINOS

On Neutrons

-

W+

Local Duality at x=1 limit breaks down at all Q2, What if we include higher resonances? And Reverse Case for antineutrinos


Two Photon Effects In radiative corrections Are NOT significant for this program.

arie bodek, univ. of rochester1 outline of a program in investigating nucleon and nuclear structure...

Documents

vector scattering

nuclear targets

antineutrino vector

neutrino reactions

nuclear structure

nuclear corrections

vector continuum f2

high q